Families of released Americans who’d long been held prisoner by Iran are rejoicing this week, but Washington hostage negotiators mustn’t relax. Their skills will soon be required again.

Jason Rezaian, Amir Hekmati and Saeed Abedini were released on Sunday. In return, seven Iranian citizens, convicted in American courts on arms-smuggling charges, were let go. Fourteen Iranian men, wanted on various charges, were also removed from Interpol’s most-wanted list.

But even as the plane that carried the finally free Americans from Iran to Switzerland landed, a new kidnapping crisis was brewing in Iraq.

Three American citizens were taken and, according to credible reports, transferred by their captors to Iraq’s Sadr City, ruled by an Iranian-backed Shiite militia headed by the ruthless Muqtada al-Sadr.

Iraqis tell a dark story: The two men and one woman were partying late into the night at an area in south Baghdad that one Iraqi source described as its “red light district.” The source speculated that while partying, the three apparently made the crucial mistake of bragging that they have American passports.

That turned them into a commodity. Despite looking and dressing as the locals do, and even though they spoke with perfect Iraqi accents, the three — employed by the United States as security contractors at a Baghdad airport — became valuable.

Such details, widely disseminated to Iraqi-based reporters, must be taken with a grain of salt. The Shiite-heavy Iraqi government is embarrassed by the kidnapping, and would gladly blame the victims for their plight.

Washington officials, rightly, declined to shed much light on the affair. Citing privacy issues, State Department spokesman John Kirby made clear this week that while “the picture is becoming a little bit more clear in terms of what might have happened,” he wouldn’t provide further details.

But State also wants to discourage any linkage between the kidnapping and Iran. Did Secretary of State John Kerry contact his new buddy Javad Zarif? Kirby, in mock surprise, answered that the kidnapping occurred in Iraq, so why should Kerry call Iran’s foreign minister?

Yes, to quote “Ali G.,” Sasha Baron Cohen’s bumbling alter ego, “It’d be a good idea if one of them changed their name, to make it different-sounding from the other one.” But serious Americans apparently don’t blame Iran for something that happened in Iraq.

Especially now that in the eyes of American officials, Iran can do no wrong. On Thursday, Kerry acted as an advocate for Iran’s supreme leader, saying that Ali Khamenei’s “apology” for a recent sacking of the Saudi embassy in Tehran was “very significant” and a “huge step.”

Yet, US citizens are now held in an Iraqi area where Iran wields much influence.

And even if there was no direct order from Tehran, the kidnappers must have believed that their Iranian patrons would be pleased. Perhaps inspired by recent footage of Iranian naval commandos holding at gunpoint the crews of two US Navy boats, they thought someone in Tehran would handsomely compensate them. The Great Satan bows again.

Whatever the reality is, the new kidnapping situation won’t be resolved without Tehran’s involvement. And indeed, on Thursday Kerry finally acknowledged that he’s asking Zarif for help. So the same DC officials who’ve toiled for months to compensate the mullahs to finally release long-held American hostages are at it again.

And once again, they’ll have to deal with the realities of Tehran’s factional politics. Zarif and President Hassan Rouhani believe that to maintain the regime’s tenuous hold on power, some necessary concessions must be made to America. On the other side, a much more powerful faction — Khamenei and his Revolutionary Guards henchmen — fear any opening to the West is detrimental for the future of the regime and push for an ever-increasing confrontation.

The business of hostage negotiation is delicate. For the hardliners, holding Americans is a tried and true tool. Sure, they’d tolerate it if Rouhani & Co. occasionally extract a heavy American price for a swap. After all, President Obama’s diplomacy aside, the Islamic Republic has yet to shed old habits. So either the Guards or some proxy can always find new hostages to start the whole process anew.